How do you simplify the expression #(x^5y^-8)/(x^5y^-6)# using the properties?

1 Answer
Aug 22, 2017

Answer:

See a solution process below:

Explanation:

First, we can use these two properties of exponents:

#x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))# and #x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))#

#(x^color(red)(5)y^color(red)(-8))/(x^color(blue)(5)y^color(blue)(-6)) => x^(color(red)(5)-color(blue)(5))/y^(color(blue)(-6)-color(red)(-8)) => x^(color(red)(5)-color(blue)(5))/y^(color(blue)(-6)+color(red)(8)) => x^0/y^2#

We can use this property to simplify the #x# term:

#a^color(red)(0) = 1#

#x^color(red)(0)/y^2 => 1/y^2#